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      SUBROUTINE <a name="SLARRA.1"></a><a href="slarra.f.html#SLARRA.1">SLARRA</a>( N, D, E, E2, SPLTOL, TNRM,
     $                    NSPLIT, ISPLIT, INFO )
      IMPLICIT NONE
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  -- LAPACK auxiliary routine (version 3.1) --
</span><span class="comment">*</span><span class="comment">     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
</span><span class="comment">*</span><span class="comment">     November 2006
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     .. Scalar Arguments ..
</span>      INTEGER            INFO, N, NSPLIT
      REAL                SPLTOL, TNRM
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Array Arguments ..
</span>      INTEGER            ISPLIT( * )
      REAL               D( * ), E( * ), E2( * )
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Purpose
</span><span class="comment">*</span><span class="comment">  =======
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Compute the splitting points with threshold SPLTOL.
</span><span class="comment">*</span><span class="comment">  <a name="SLARRA.22"></a><a href="slarra.f.html#SLARRA.1">SLARRA</a> sets any &quot;small&quot; off-diagonal elements to zero.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Arguments
</span><span class="comment">*</span><span class="comment">  =========
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  N       (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The order of the matrix. N &gt; 0.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  D       (input) REAL             array, dimension (N)
</span><span class="comment">*</span><span class="comment">          On entry, the N diagonal elements of the tridiagonal
</span><span class="comment">*</span><span class="comment">          matrix T.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  E       (input/output) REAL             array, dimension (N)
</span><span class="comment">*</span><span class="comment">          On entry, the first (N-1) entries contain the subdiagonal
</span><span class="comment">*</span><span class="comment">          elements of the tridiagonal matrix T; E(N) need not be set.
</span><span class="comment">*</span><span class="comment">          On exit, the entries E( ISPLIT( I ) ), 1 &lt;= I &lt;= NSPLIT,
</span><span class="comment">*</span><span class="comment">          are set to zero, the other entries of E are untouched.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  E2      (input/output) REAL             array, dimension (N)
</span><span class="comment">*</span><span class="comment">          On entry, the first (N-1) entries contain the SQUARES of the
</span><span class="comment">*</span><span class="comment">          subdiagonal elements of the tridiagonal matrix T;
</span><span class="comment">*</span><span class="comment">          E2(N) need not be set.
</span><span class="comment">*</span><span class="comment">          On exit, the entries E2( ISPLIT( I ) ),
</span><span class="comment">*</span><span class="comment">          1 &lt;= I &lt;= NSPLIT, have been set to zero
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  SPLTOL (input) REAL            
</span><span class="comment">*</span><span class="comment">          The threshold for splitting. Two criteria can be used:
</span><span class="comment">*</span><span class="comment">          SPLTOL&lt;0 : criterion based on absolute off-diagonal value
</span><span class="comment">*</span><span class="comment">          SPLTOL&gt;0 : criterion that preserves relative accuracy
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  TNRM (input) REAL            
</span><span class="comment">*</span><span class="comment">          The norm of the matrix.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  NSPLIT  (output) INTEGER
</span><span class="comment">*</span><span class="comment">          The number of blocks T splits into. 1 &lt;= NSPLIT &lt;= N.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  ISPLIT  (output) INTEGER array, dimension (N)
</span><span class="comment">*</span><span class="comment">          The splitting points, at which T breaks up into blocks.
</span><span class="comment">*</span><span class="comment">          The first block consists of rows/columns 1 to ISPLIT(1),
</span><span class="comment">*</span><span class="comment">          the second of rows/columns ISPLIT(1)+1 through ISPLIT(2),
</span><span class="comment">*</span><span class="comment">          etc., and the NSPLIT-th consists of rows/columns
</span><span class="comment">*</span><span class="comment">          ISPLIT(NSPLIT-1)+1 through ISPLIT(NSPLIT)=N.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  INFO    (output) INTEGER
</span><span class="comment">*</span><span class="comment">          = 0:  successful exit
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Further Details
</span><span class="comment">*</span><span class="comment">  ===============
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Based on contributions by
</span><span class="comment">*</span><span class="comment">     Beresford Parlett, University of California, Berkeley, USA
</span><span class="comment">*</span><span class="comment">     Jim Demmel, University of California, Berkeley, USA
</span><span class="comment">*</span><span class="comment">     Inderjit Dhillon, University of Texas, Austin, USA
</span><span class="comment">*</span><span class="comment">     Osni Marques, LBNL/NERSC, USA
</span><span class="comment">*</span><span class="comment">     Christof Voemel, University of California, Berkeley, USA
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  =====================================================================
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     .. Parameters ..
</span>      REAL               ZERO
      PARAMETER          ( ZERO = 0.0E0 )
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Local Scalars ..
</span>      INTEGER            I
      REAL               EABS, TMP1

<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Intrinsic Functions ..
</span>      INTRINSIC          ABS
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Executable Statements ..
</span><span class="comment">*</span><span class="comment">
</span>      INFO = 0

<span class="comment">*</span><span class="comment">     Compute splitting points
</span>      NSPLIT = 1
      IF(SPLTOL.LT.ZERO) THEN
<span class="comment">*</span><span class="comment">        Criterion based on absolute off-diagonal value
</span>         TMP1 = ABS(SPLTOL)* TNRM
         DO 9 I = 1, N-1
            EABS = ABS( E(I) )
            IF( EABS .LE. TMP1) THEN
               E(I) = ZERO
               E2(I) = ZERO
               ISPLIT( NSPLIT ) = I
               NSPLIT = NSPLIT + 1
            END IF
 9       CONTINUE
      ELSE
<span class="comment">*</span><span class="comment">        Criterion that guarantees relative accuracy
</span>         DO 10 I = 1, N-1
            EABS = ABS( E(I) )
            IF( EABS .LE. SPLTOL * SQRT(ABS(D(I)))*SQRT(ABS(D(I+1))) )
     $      THEN
               E(I) = ZERO
               E2(I) = ZERO
               ISPLIT( NSPLIT ) = I
               NSPLIT = NSPLIT + 1
            END IF
 10      CONTINUE
      ENDIF
      ISPLIT( NSPLIT ) = N

      RETURN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     End of <a name="SLARRA.128"></a><a href="slarra.f.html#SLARRA.1">SLARRA</a>
</span><span class="comment">*</span><span class="comment">
</span>      END

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